Are these problems showing up on the new fronds? The old damaged fronds won't become better, but will be replaced. So they'll continue to show the hard time they had until they finally die off. Hopefully by that stage the plant will have a full set of new healthy ones.

Burns on new fronds could be the result of over fertilising. They may have been affected while they were developing before you got the plant. So make sure the soil is fast draining. Don't let it get soggy. And you can flush out excess salts/fertiliser with water (provided your soil drains well).